He later admitted: "The maintenance of the no-deal option is for negotiating reasons."

Image:Mr Davis is locked in talks with Mr Barnier

The split threatens to undermine Theresa May's repeated insistence that "no deal is better than a bad deal" and re-open divisions between Tory MPs that backed Remain and Leave in the EU referendum.

Conservative MP James Duddridge appeared to directly criticise Ms Rudd, telling Sky News: "Far from being unthinkable, no deal would be my preferred choice to achieve a fast, clean and boring Brexit.

"The sooner we get on with it, the better."

Remain-supporting Labour MP Chuka Umunna also hit out at the split between Ms Rudd and Mr Davis, claiming it was "increasing the likelihood of our country crashing out of the EU with an extreme, destructive Brexit".